In Death of a Salesman and Of Mice and Men, how do the characters' dreams lead to their ultimate demise?

In Death of a Salesman, Willy Loman (get it? "low man"?) exemplifies the American Dream of getting out of poverty by pulling yourself up by your own bootstraps. A career in sales was hailed as the best way to do that, and so Willy takes to it with gusto. Since he believes that he can achieve success through manipulating and charming those around him, he cultivates those qualities in himself and his children, Biff and Happy. Unfortunately, in Willy's dedication to this narrative of success, he refuses to acknowledge it is flawed until it's too late – if indeed he ever does. Biff sums up the reason for Willy's lack of success and eventual downfall in Act 2: 

"I am not a leader of men, Willy, and neither are you. You were never anything but a hard-working drummer who landed in the ash can like the rest of them! I’m one-dollar an hour, Willy! I tried seven states and couldn’t raise it. A buck an hour! Do you gather my meaning? I’m not bringing home any prizes anymore and you’re going to stop waiting for me to bring them home!"

As Willy realizes that neither he nor his sons will ever succeed, he begins to think that the best course of action is to kill himself in a car accident so his family can benefit from the insurance money. Even this plan, however, is framed as his "next big break," with his older brother Ben urging him towards the "diamonds" that made Ben rich (code for insurance money). Even at the end, Willy is looking for the magic key to success. 

In Of Mice and Men, George and Lennie dream of owning a farm together someday, where Lennie can keep rabbits. The way we see them reference that dream in their day-to-day life as migrant farm workers, though, suggests that it's more a fantasy than a realistic possibility for the pair. The way Lennie begs George to go over the details of the dream again and again makes it seem more like a soothing story than anything they could actually do. 

However, I would disagree that George and Lennie's dream of a farm leads to their demise. Rather, I would say that their demise comes from the loss of the possibility of achieving their dream. They seem to know it's unlikely, but when Candy offers his life savings as part of a down payment, it starts to seem real. Therefore, when Lennie messes up again and accidentally kills Curly's wife, the realization that their dream will never come true hits them even harder. This loss is summed up in the following dialogue after Lennie kills Curly's wife:

"Lennie said, 'George.'

'Yeah?'

'I done another bad thing.'

'It don't make no difference,' George said, and he fell silent again."

George seems to accept the fact that the dream of a farm could never come true. Still, it was like a beacon of hope to keep him and Lennie going through the drudgery and hard work of each day. With the loss of their dream, they are faced with the full ramifications of the Great Depression – all of the despair and struggle that so many working men faced.